Exploiting all phone media? A multidimensional network analysis of phone users sociality

The growing awareness that human communications and social interactions are assuming a stratified structure, due to the availability of multiple techno-communication channels, including online social networks, mobile phone calls, short messages (SMS) and e-mails, has recently led to the study of multidimensional networks, as a step further the classical Social Network Analysis. A few papers have been dedicated to develop the theoretical framework to deal with such multiplex networks and to analyze some example of multidimensional social networks. In this context we perform the first study of the multiplex mobile social network, gathered from the records of both call and text message activities of millions of users of a large mobile phone operator over a period of 12 weeks. While social networks constructed from mobile phone datasets have drawn great attention in recent years, so far studies have dealt with text message and call data, separately, providing a very partial view of people sociality expressed on phone. Here we analyze how the call and the text message dimensions overlap showing how many information about links and nodes could be lost only accounting for a single layer and how users adopt different media channels to interact with their neighborhood.

💡 Research Summary

The paper presents the first large‑scale multiplex analysis of mobile phone users by jointly considering voice calls and short text messages (SMS). Using Call Detail Records (CDRs) from a major European mobile operator, the authors collected 63 million call records and 20 million SMS records over a 12‑week period (March 26–May 31, 2012). After anonymising subscriber identifiers and filtering out interactions with other operators, they retained only intra‑operator communications. To focus on socially meaningful ties, they further filtered the data: a call pair was kept only if the total call duration exceeded one minute and the pair exchanged more than three interactions; an SMS pair was kept if it exchanged more than three messages. The resulting dataset comprises roughly 253 000 active users, 7 million filtered calls (≈317 000 h of conversation) and 4 million SMS.

The authors model the system as an edge‑labelled directed multigraph G = (V, E, D, ℓ) where D = {c, s} denotes the two layers (c = call, s = SMS). Each directed edge (u, v, d) carries a label ℓ(u, v, d) = ⟨f_c(u,v), δ(u,v)⟩ for calls and ⟨f_s(u,v)⟩ for SMS, where f_* are the numbers of interactions and δ is the aggregated call duration. From G they extract the single‑layer graphs G_c (call graph) and G_s (SMS graph) and also analyse the combined multiplex G.

Basic structural statistics (Table 1) show that G_c contains 228 208 nodes and 467 290 directed edges, while G_s has 159 610 nodes and 298 136 edges. The multiplex G has 253 180 nodes and 589 127 edges. The giant weakly connected component (GWCC) of G includes all nodes, but the giant strongly connected component (GSCC) is much smaller: only 75 nodes in G_c, 2 040 in G_s, and 4 611 in the multiplex. Thus, relying on a single layer would miss roughly 20 % of nodes in the strongly connected core and about 10 % of the overall user base.

Node overlap analysis reveals that 30 % of users appear only in the call layer (|V_c − V_s| = 162 296), 8 % only in the SMS layer (|V_s − V_c| = 18 621), and 62 % are present in both layers (|V_c ∩ V_s| = 253 689). To capture more nuanced behavior, the authors introduce a layer‑specific Jaccard distance φ for each user u:

φ_{d1,d2}^{+}(u) = |Γ^{+}{d1}(u) − Γ^{+}{d2}(u)| / |Γ^{+}{d1}(u) ∩ Γ^{+}{d2}(u)|,

with analogous definition for incoming neighborhoods (−). Here Γ^{+}_{d}(u) denotes the set of out‑neighbors of u in layer d. Empirical distributions of φ^{+}{c,s} and φ^{−}{c,s} show that about 40 % of users have φ close to 1, meaning they interact almost exclusively via calls, while roughly 30 % use both media for more than 70 % of their contacts. SMS is therefore a secondary channel, primarily used for a subset of relationships.

Link overlap is examined by treating any directed pair that appears in at least one layer as a single multiplex edge. The multiplex contains 333 439 unique directed pairs, compared with 263 485 in the call layer and 173 091 in the SMS layer. Consequently, about 28 % of directed pairs are missing if only calls are considered, highlighting the complementary role of SMS in revealing otherwise hidden social ties.

The paper’s contributions are threefold: (1) a methodological framework for constructing and analysing large‑scale multiplex mobile communication networks; (2) the definition of an edge‑labelled directed multigraph and the layer‑specific Jaccard distance, enabling fine‑grained assessment of users’ media preferences; (3) empirical evidence that single‑layer analyses substantially underestimate the size and connectivity of mobile social networks, with implications for information diffusion, epidemic modeling, and targeted marketing.

In conclusion, integrating both voice calls and SMS provides a richer, more accurate portrait of mobile sociality. The authors suggest future extensions to incorporate additional digital channels (e.g., instant messengers, social media), temporal dynamics, and layer‑specific diffusion models, thereby advancing both the theory of multiplex networks and its practical applications in sociology, epidemiology, and business analytics.